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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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=
AB
Nocandum autem est, quod in trianeulo Obtusanculo, si ab utrovis acutorum an-
sulorum demittatur perpendicularis (ut nempe angutus ille acutus, puta B, habea-
tur pro vertice criansuli, ec laterum breviorum alterum, CB, pro bale,) perpers-
dicularis illa (Duca BP.) cadet extra expositum trianculum in basin productam;
(quod Creometrice, li opus lu, Facile elt probacu:) inrariata tamen praececentis
regulae veritate; quae quidem hie Subductione collisitur, licur in praecedente ex-
emplo Additione. Ouod lic oltenditur.
Friansuli BF. B rectanguli (propier angulum rectum adF, demilsa vervendi
culari tactum,) area habetur ex ductu alticudinis BF in Z P B, lemiem basis:
Trianguli vero BF. C (pari de caula) ex ductu ejusdem altcudins BF. in L F. C
Temissem balis fux; Ilorum icaque triangulorum ditterentia, quod est ixtum irian-
sulum BCB expolicum, Cs ZF BXBF. = Z F. C. XBF., quod tancundem est arque
ER. B = ZF C. (hoc CA = CB) in BF. (NaM F. B - F. C = CB, ideoque : L B -
SEC = ECB, ve) E. B = EC
Semilsi alcicudinis in balin ductae.
E.). Iaque et hoc pacto emerget area aequalio
ZF. B- ZF. C = = CB
XBF.
ZLBRBE =ZECKBF = E CBXBF.
Sect et idem aliter oltenditur; (Acque eadem opera, non modo Friangulum re.
Etangulum, quod modo dictum cAt, Led ee Trianculum quodvis rectilneum esse
Paralleloerammi dimidium.) Si Friangulum expolicum BCB (sive Rectangulum,
lire acucansulum, live obculangulum) Cuper bali BB consticurum (ita nempe ut
perpendicularis a verrice cadat intra Priangulum) inscribatur Parallelogrammo
Rectansulo luper eadem bale, eandem item alcicudinem habenti cum iplo crian.
sulo, nempe DB. Cum enim criansula rectangula C A B, C AB, linc ligillatim x.
qualia semiltibus parallelogrammorum AD, AS; erit d aggregatum illorum, hoc
Clt, Friangulum BCB, semilti torius DB parallelogrammi (ex duobus AD, AS,
aggregati) aequale.
Sin exrra criangulum cadat perpendicularis (quod in triangulo Obtusansulo
tieri posse diximus) illud idem oltendicur hoc pacto. Completo parallelocrammo
BCB7 (ductis nempe B7, B7, laceribus trianguli BC, BC, parallelis) crunc duo
criangula BCB, By B, inricem Cumilia et aqualia, et prope
Grammi semisTis: AF paralselosrammum illud aeguacur rectangulo, alciciidine BF.
velyc, e bali CB vel By, comprehenso (uc supta oltentum elt,) erso Friangulum
ejuldem semissi aquatur: nempe semisti quancitacis factae ex ductu balis C. B in alci-
cudinem B F, vel quancitari factae ex duetu semillis balis in coram alcicudinem, vel
semissis alcirudinis in coram balin; quae omni cancundem ralent; quippe
Trianeuli
cujus vis.
EBXBL
=hCBKBF. = CB~L BF.
Patet isitur unirertim emodus tenturandi Lrianculum quodvis (live Rectan.
oulum sive Obculansulum sive Acucangulum) Nempe, a quovis ipsius aneulo de
missa in latus oppositum (productum, li opuS,) perpendiculari; harum rectarum
(IciL. perpendicularis, ec dicti lateris,) si altera in alterius semissem ducatur, prodi-
bit area Trianguli. Contra vero; Si areae duplum per earum rectarum alteram
dividatur, habetur reliqua: puta Si per balin, haberur pervendicularis sive alcicudo:
Nensu- E per aleicudinem, habecur batis. Aeque de Frrangulis menturandis hactenus.
ratio si
Eutae c-
jusvisre
etilinea
Expolica jam mechodo menturandi quodvis Cire Parallelogrammum sive Frian-
sulum; eadem opera et tisuras alias rectilimeas qualeunque menlurare docuimus:
Talrem E illud addacur Preuram quamvis rectilineam vel in Paralleloeramma di-
vidi posse, vel saltem in Trianeula: Six quorum igitur caleulo, proposicae tigurae
calculus stacim innoreseit.
Exempli